A new alternating direction method for co-coercive variational inequality problems

Abstract. In this paper, we propose a new alternating direction method for solving cocoercive variational inequality problems VI(f, S) with both linear equality and inequality constraints without the need to add any extra slack variables. We focus on the underlying function f does not have an explicit form and only its function values can be employed in the new method. Under the condition that the underlying function f is co-coercive, we prove the convergence of the new method. Preliminary numerical experiments are included to illustrate the efficiency of the new method.